Shake hands

Probability Level 1

There is a class of 50 students. In the morning 1st student comes and sits in the class. 2nd comes and shake hand with the 1st one. Then 3rd comes and shake hands with the both and so on.... How many hand shakes would be there till the last student comes?


The answer is 1225.

Dikshant Chadha by Dikshant Chadha , 22, India

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2 solutions

Sunil Pradhan
Aug 12, 2014

No. of shake hands = n(n – 1)/2 = 50 × 49/2 = 1225

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Kavi Murasu
Jul 4, 2014

1+2+......+49=1225 50 th student is not included inthe sum bcoz he is the one who finally shakes hands with everyone

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49 students come and shake hands with first student. 2nd student shakehands wiyh first and 48 others shake hands with the second student. Similarly every student is involved in 49 handshakes. And since every handshake is counted twice (from perspective of both people involved in a handshake), Therefore, total handshakes = (49x50)/2 = 1225

utkarsh goel - 6 years, 11 months ago

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